Data-Driven Control of Continuous-Time LTI Systems via Non-Minimal Realizations

This article proposes an approach to design output-feedback controllers for unknown continuous-time linear time-invariant systems using only input-output data from a single experiment. To address the lack of state and derivative measurements, we introduce non-minimal realizations whose states can be observed by filtering the available data. We first apply this concept to the disturbance-free case, formulating linear matrix inequalities (LMIs) from batches of sampled signals to design a dynamic, filter-based stabilizing controller. The framework is then extended to the problem of asymptotic tracking and disturbance rejection—in short, output regulation—by incorporating an internal model based on prior knowledge of the disturbance/reference frequencies. Finally, we discuss tuning strategies for a class of multi-input multi-output systems and illustrate the method via numerical examples.